Newbetuts

Is there a general identity for the infinite radicals; $\sqrt{n^{0}+\sqrt{n^{1}+\sqrt{n^{2}+\sqrt{n^{3}+...}}}}$

Is there a closed form for $3\cdot\frac{3}{\sqrt{6}}\cdot\frac{3}{\sqrt{6+\sqrt{6}}}\cdot\frac{3}{\sqrt{6+\sqrt{6+\sqrt{6}}}}\cdots$?

How would you prove $\int^8_0\frac1{\sqrt{x+\frac1{\sqrt{x}}}}dx<4-\frac1{2019}$?

Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

Find $\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$

Simplifying $\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}$

How to show that $\sqrt{3 - \sqrt{2}} \notin \mathbb{Q}(\sqrt{3 + \sqrt{2}})$ [duplicate]

Why does $\sqrt{n\sqrt{n\sqrt{n \ldots}}} = n$?

Nested sine and cosine half angle formulas [closed]

How do you simplify this square root of sum: $\sqrt{7+4\sqrt3}$?

Yet another nested radical

How to arrive at Ramanujan nested radical identity

An incorrect answer for an integral

Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction

Unsure of my work evaluating $\int \frac{dx}{\sqrt{x + \sqrt{x + \sqrt{x + \cdots}}}}$

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.

New posts in nested-radicals

Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2 [duplicate]

Finding a root of a degree 5 polynomial

How to evaluate $\lim_{x \to \infty}\left(\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}\right)$?

Closed form for $\sqrt{1+\sqrt[2!]{2^2+\sqrt[3!]{3^3+...}}}$

Is there a general identity for the infinite radicals; $\sqrt{n^{0}+\sqrt{n^{1}+\sqrt{n^{2}+\sqrt{n^{3}+...}}}}$

Is there a closed form for $3\cdot\frac{3}{\sqrt{6}}\cdot\frac{3}{\sqrt{6+\sqrt{6}}}\cdot\frac{3}{\sqrt{6+\sqrt{6+\sqrt{6}}}}\cdots$?

How would you prove $\int^8_0\frac1{\sqrt{x+\frac1{\sqrt{x}}}}dx<4-\frac1{2019}$?

Why is $\sqrt[3]{18+5\sqrt{13}} + \sqrt[3]{18-5\sqrt{13}} = 3$?

Find $\lim_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\sqrt[4]{4+\ldots+\sqrt[n]{n}}}}$

Simplifying $\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}$

How to show that $\sqrt{3 - \sqrt{2}} \notin \mathbb{Q}(\sqrt{3 + \sqrt{2}})$ [duplicate]

Why does $\sqrt{n\sqrt{n\sqrt{n \ldots}}} = n$?

Nested sine and cosine half angle formulas [closed]

How do you simplify this square root of sum: $\sqrt{7+4\sqrt3}$?

Yet another nested radical

How to arrive at Ramanujan nested radical identity

An incorrect answer for an integral

Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction

Unsure of my work evaluating $\int \frac{dx}{\sqrt{x + \sqrt{x + \sqrt{x + \cdots}}}}$

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.